This paper derives the relative air-gap-specific permeance distribution function by Schwarz-Christoffel Transformation, considering the effect of slotting. Neglecting the iron saturation, and employing the analytical algorithm for partial differential equations, efficient and effective analytical calculations of no-load air-gap magnetic field distribution, armature field distribution, and phase electromotive force (EMF), are demonstrated, considering the stator slots. Subsequently, based on the main circuit topology of a brushless dc motor (BLDCM), the field-circuit coupling model is constructed for the motor, and then the phase current waveforms and load air-gap magnetic field distribution at any time are determined. Consequently, the instantaneous electromagnetic torque is computed, which underpins the quantitative analysis of torque ripple and the pulsation induced by commutation. Hence, the present work paves the way to precise prediction of the motor's performance and acoustic noise. It is a powerful tool for the design of surface permanent magnet brushless dc motors.